Welcome back math geeks!
I love teaching young students about data and statistics. And I enjoy finding ways to make data and statistics matter more to young students. But I’m troubled by two curriculum practices about how we teach students to think about data and statistics, especially at the K-6 level. This post is Part 2. In my first post, I wrote about how data is often represented to students in heavily scaffolded textbook pages that rob students of the opportunity to purposely engage in thinking, wondering, and discourse…and a solution to this practice. (If you missed Part 1, click here.)
In this post, I’ll outline another troubling practice and my attempt to help to teachers work around this obstacle.
Troubling Practice #2
The progression for Measurement and Data begins in Kindergarten and coherently builds through 5th grade. Starting in 1st grade, students are expected to represent and interpret data. But the “represent and interpret data” standards are never a part of the focus clusters. At every grade level (from 1st through 5th grade), “represent and interpret data” is listed only as a supporting cluster. In grades 6th-8th, all of the statistics and probability standards are listed as supporting clusters or additional clusters.
As a result, these standards are often to pushed to the back of textbooks and are the last topics in the curriculum scope and sequence for the year. At best, data and statistics content gets shallow lip service with a few lessons at the end of the year. At worst, it’s possible that a student could arrive to high school with hardly any exposure to the joy, wonder, and utility of reasoning about data and using statistical tools to find patterns.
And this sucks. Partly because data science is an exploding professional field and we’re not creating the type of curious and inquisitive students that will go on to to fill those jobs. Partly because our democracy is stronger when its citizens can think critically for themselves and determine which statistics are outright lies and which statistics might be true. And partly because it’s fun teaching students about data and statistics! It can be such an engaging topic that focuses on discourse, asking questions, and making arguments.
A Solution: Making Estimation Matter More
I try to address this troublesome practice by finding authentic opportunities for teachers to embed data into existing lessons. After all, the purpose of the supporting and additional clusters is to engage students in deepening their understanding of the major clusters. I’d like to share with you one particular tool I like to use to do this.
When doing 3-Act Math lessons or an Estimation180 activity, I like to capture as many student estimations as I can. Estimating invites students to engage more with a problem, lowers the floor for learners, provides space for discussion and debate, and fosters student ownership as they embrace and seek to resolve ambiguity. Once a thoughtful guess is made, we often want to see if we’re right.
Once the estimations are collected and displayed to the whole class, interesting conversations can happen. What appears to be the “class estimate?” How do we define what we mean by “class estimate” and how do we find it’s value? Is our data clustered or is our data spread over a wide range? What does this mean about our level of agreement?
While interpreting measures of center and measures of spread are not standards until the 6th grade, these types of questions can lead to interesting observations worth talking about in any class. And they are accessible to elementary school students. Furthermore, they help students become familiar with line plots and how to interpret them, an explicit standard in 4th and 5th grade.
Lastly, this practice invites the community into a intellectual space as they share their thinking about a common question. They become mathematicians and scientists making observations, questioning assumptions, pondering different variables, thinking flexibility, talking to one another. Furthermore, collective group estimates are often (but not always) more accurate than an individual’s estimate. (Note: This is a real thing called the “Wisdom of the Crowd.”) And as they continue to make estimates throughout the year, they can monitor their growth as a community of learners. More on this in a moment.
A Data Tool to Graph Estimates
Capturing 30 student responses and displaying them is not an efficient task and is a costly allocation of 5-7 minutes of instructional time. I’ve been seeking a tool that could help. And I’ve found one: CODAP.
The Common Online Data Analysis Platform (CODAP) is not a name that inspires a teacher to use it. It sounds like something biologists or world health organizers might use, not elementary school teachers.
But hang in there. It’s simple to use. It’s free. It works. I have a video (ok a few videos) that show you how.
In this video, you’ll see how to enter in student estimates and make a dot plot of classroom estimates.
(Click here if viewing on your phone.)
Essentially, all you need to do is load CODAP on your web browser, input student estimates, create a blank graph, and then drag those estimates on to the x-axis. And voila. A visual of classroom estimates to use in discussion. You can graph the mean, median, and a box plot too if you’d like.
In the previous video, you may have noticed that it took some time for me to input student estimates in to CODAP. If you have 3 minutes of planning time to spare, you can streamline this process by creating a Google Survey for your students to use. In this video, I show you how to do this and how to then input that data in to CODAP.
(Click here if viewing on your phone.)
In this video, you’ll learn how to use CODAP to monitor classroom growth over time. This CODAP file will let you show the margin of error (how close the class estimate was to the actual answer) over the course of a school year. By having a discussion around margin of error and being able to see their progress, students will become more vested in improving their estimating and quantitative reasoning skills.
(Click here if viewing on your phone.)
Here’s a link to the CODAP file for the classroom list. Just create a copy and save the file for your own use.
Invitation to Collaborate
Thanks for hanging in there. There’s a lot in this post. But I hope you’re seeing how CODAP can be a tool to leverage student estimations to push in more authentic conversations about data and statistics while also teaching the major clusters. This tool can be a 10 minute conversation piece once or twice a week as students are doing 3-Act Math lessons or an Estimation180 activity.
Let me know how you make use of this. Let me know how I can make this process clearer. Let’s get better together.
